# Dynamic Rotation Total Torque Calculation

• inner08
In summary, the problem involves two blocks connected by a cord passing through a pulley with given masses and dimensions. The goal is to find the total torque on the system, the kinetic moment of the system, and the acceleration of the blocks using the equation torque(ext)=dL/dt. The solution involves drawing a free body diagram and isolating the angular acceleration, then substituting it into the torque equation to find the correct answer.
inner08

## Homework Statement

Two blocks of mass m1=3kg and m2=5kg are linked by a cord passing through a pulley of radius R=8cm and of mass M=4kg. We neglect friction and we assimilate the pulley to a disk. We place the origin at the center of the pulley.

a) what is the total torque on the system?
b) what is the kinetic moment (I hope I translated it correctly..its moment cinetique in french) of the system when the blocks have a speed of v?
c) Find the acceleration of the blocs by applying the equation torque(ext)=dL/dt.

## Homework Equations

torque(ext)=dL/dt
T1-T2= Ia
a = alpha * r

## The Attempt at a Solution

I drew a fbd and came up with this:

m1: T1-m1*g=m1*a
m2: m2*g - T2 = m2*a
pulley: T2 - T1 = I(alpha)

I figured i'd try to isolate alpha and then substitute it in the equation T1-T2 to find the torque.

m2*g - m2*a - (m1*a + m1*g) = I * alpha
5 * 9.8 - 5a - 3a - 3*9.8 = (1/2)MR^2 * alpha
49 - 8a - 29.4 = (1/2)4*0.08^2 * alpha
19.6 - 8a = 0.0128 * alpha
19.6 - 8(alpha*r) = 0.0128 *alpha
19.6 - .64alpha = 0.0128alpha
19.6 = 0,6528alpha
alpha = 30

Substitute alpha in the equation torque = T2 - T1

19.6 - .64 * 30 = 0.4 <-- this is wrong..it should be 1.57

You are being asked for the torque acting on the system, not the torque acting on the wheel. This problem is a but unusual. It wants you to look at the angular momentum of the whole system relative to the origin and the effect of external torques acting on that system

I would first commend the student for their attempt at solving the problem and using the correct equations. However, there are a few errors in their approach.

Firstly, in the equation for the pulley, the student has incorrectly multiplied the moment of inertia (I) by alpha. The correct equation is T2-T1=I*alpha*r, where r is the radius of the pulley.

Secondly, in the calculation for alpha, the student has used the wrong units for the moment of inertia. It should be in kg*m^2, not cm^2.

Lastly, in the final calculation for the torque, the student has used the wrong value for alpha. It should be 30 radians/s^2, not 30.

Overall, the student's approach is correct, but they need to pay closer attention to units and use the correct values in their calculations. The correct answer for the torque should be 1.57 Nm.

## 1. What is dynamic rotation total torque calculation?

Dynamic rotation total torque calculation is a mathematical process used to determine the total torque required in a rotating system, taking into account factors such as the mass, velocity, and angular acceleration of the system.

## 2. Why is dynamic rotation total torque calculation important?

Dynamic rotation total torque calculation is important because it allows scientists and engineers to accurately design and predict the performance of rotating systems, such as engines, turbines, and motors. It also helps ensure the safety and efficiency of these systems.

## 3. How is dynamic rotation total torque calculated?

Dynamic rotation total torque is calculated using the equation τ = Iα, where τ is the total torque, I is the moment of inertia, and α is the angular acceleration. The moment of inertia can be calculated by taking the sum of the mass of each object in the system multiplied by the square of its distance from the axis of rotation.

## 4. What are some applications of dynamic rotation total torque calculation?

Dynamic rotation total torque calculation is used in a variety of applications, including but not limited to: designing and optimizing engines and motors, calculating the stability of rotating structures such as wind turbines, and predicting the performance of vehicles and aircraft.

## 5. Are there any limitations to dynamic rotation total torque calculation?

Yes, there are limitations to dynamic rotation total torque calculation. It assumes that the system is rigid and has uniform mass distribution, which may not always be the case in real-world situations. Additionally, it does not take into account external factors such as friction or air resistance, which can affect the total torque in a system.

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